Where's good to go?
Just walk around. It's all pretty. Wouldn't bother with the Jorvik Centre personally, but there's the museum and the art gallery which are both decent. Oh, and go to the Minster, it's great.

Where's good to eat?
SO many great places. My advice would be to find a street called 'Fossgate' and work your way down - in particular 'Khao San Road' (Thai), 'Barbakan' (Polish), and 'Meltons Too'. If you want to splash out try J Bakers.
Also the Picturehouse Cinema is great - good food there, and the music venue downstairs called the basement is a favourite of mine.

Where's good to drink?
Jesus, where do I start. There's about a million decent real ale pubs in the centre. My faves are the York Brewery bars (The Last Drop, Three-Legged Mare, and Yorkshire Terrier), Lamb & Lion, Guy Fawkes, Three Tuns... try The Phoenix if don't mind a little walk out of the city centre.